Codes with Locality for Two Erasures

In this paper, we study codes with locality that can recover from two erasures via a sequence of two local, parity-check computations. By a local parity-check computation, we mean recovery via a single parity-check equation associated to small Hamming weight. Earlier approaches considered recovery in parallel; the sequential approach allows us to potentially construct codes with improved minimum distance. These codes, which we refer to as locally 2-reconstructible codes, are a natural generalization along one direction, of codes with all-symbol locality introduced by Gopalan \textit{et al}, in which recovery from a single erasure is considered. By studying the Generalized Hamming Weights of the dual code, we derive upper bounds on the minimum distance of locally 2-reconstructible codes and provide constructions for a family of codes based on Tur\'an graphs, that are optimal with respect to this bound. The minimum distance bound derived here is universal in the sense that no code which permits all-symbol local recovery from $2$ erasures can have larger minimum distance regardless of approach adopted. Our approach also leads to a new bound on the minimum distance of codes with all-symbol locality for the single-erasure case.Comment: 14 pages, 3 figures, Updated for improved readabilit

In vitro anti-inflammatory and phytochemical properties of crude ethyl acetate extract of Baliospermum montanum Leaf (Muell – Arg)

Baliospermum montanum (Muell – Arg) which belong to Euphorbiaceae family is a well known perennial herb in Indian medicine used to treat various disorders like asthma, bronchitis, purgative, anthelmintic, diuretic, diaphoretic, rubefacient and tonic. The anti-inflammatory activity of four different solvent extracts of B. montanum leaf was investigated in Phytohaemagglutinin (PHA) induce peripheral blood mononuclear cells (PBMC) cells using MTT assay. Among the samples, ethyl acetate extract revealed good anti-inflammatory response comparatively with other extracts such as hexane, acetone, methanol and the preliminary screening of phytochemical test was investigated. The results of phytochemical screening revealed the presence of flavonoids, tannin, steroids, glycosides, amino acid and carbohydrates. Our study demonstrates that the ethyl acetate extracts of B. montanum leaves contains effective  anti-inflammatory agents, which could ultimately be used as functional material and traditional remedy against inflammation.Keywords: Baliospermum montanum, anti-inflammatory, MTT assay, phytochemical African Journal of Biotechnology Vol. 12(39), pp. 5743-574

Structure and variability in the corona of the ultrafast rotator LO Peg

Low-mass ultrafast rotators show the typical signatures of magnetic activity and are known to produce flares, probably as a result of magnetic reconnection. As a consequence, the coronae of these stars exhibit very large X-ray luminosities and high plasma temperatures, as well as a pronounced inverse FIP effect. To probe the relationship between the coronal properties with a spectral type of ultra-fast rotators with rotation period P < 1d, we analyse the K3 rapid-rotator LO Peg observed with XMM-Newton and compare it with other low-mass rapid rotators of spectral types G9-M1. We investigate the temporal evolution of coronal properties like the temperatures, emission measures, abundances, densities and the morphology of the involved coronal structures. We find two distinguishable levels of activity in the XMM-Newton observation of LO~Peg, which shows significant X-ray variability both in phase and amplitude, implying the presence of an evolving active region on the surface. The X-ray flux varies by 28%, possibly due to rotational modulation. During our observation, a large X-ray flare with a peak X-ray luminosity of 2E30 erg/s and an energy of 7.3E33 erg was observed. At the flare onset we obtain clear signatures for the occurrence of the Neupert effect. The flare plasma also shows an enhancement of iron by a factor of 2 during the rise and peak phase of the flare. Our modeling analysis suggests that the scale size of the flaring X-ray plasma is smaller than 0.5 R_star. Further, the flare loop length appears to be smaller than the pressure scale height of the flaring plasma. Our studies show that the X-ray properties of the LO~Peg are very similar to those of other low-mass ultrafast rotators, i.e., the X-ray luminosity is very close to saturation, its coronal abundances follow a trend of increasing abundance with increasing first ionisation potential, the so-called inverse FIP effect.Comment: 11 pages, 15 figures and 4 tables. Accepted for publication by Astronomy and Astrophysic

X-raying the coronae of HD~155555

We present an analysis of the high-resolution Chandra observation of the multiple system, HD 155555 (an RS CVn type binary system, HD 155555 AB, and its spatially resolved low-mass companion HD 155555 C). This is an intriguing system which shows properties of both an active pre-main sequence star and a synchronised (main sequence) binary. We obtain the emission measure distribution, temperature structures, plasma densities, and abundances of this system and compare them with the coronal properties of other young/active stars. HD 155555 AB and HD 155555 C produce copious X-ray emission with log Lx of 30.54 and 29.30, respectively, in the 0.3-6.0 keV energy band. The light curves of individual stars show variability on timescales of few minutes to hours. We analyse the dispersed spectra and reconstruct the emission measure distribution using spectral line analysis. The resulting elemental abundances exhibit inverse first ionisation potential effect in both cases. An analysis of He-like triplets yields a range of coronal electron densities ~10^10-10^13 cm-3. Since HD 155555 AB is classified both as an RS CVn and a PMS star, we compare our results with those of other slightly older active main-sequence stars and T Tauri stars, which indicates that the coronal properties of HD 155555 AB closely resemble that of an older RS CVn binary rather than a younger PMS star. Our results also suggests that the properties of HD 155555 C is very similar to those of other active M dwarfs.Comment: 17 pages, 23 figues, Accepted in Ap

Sub-inverse and g-inverse of an Intuitionistic Fuzzy Matrix using Bi-implication Operator

In this paper, we introduce a bi-implication operator for intuitionistic fuzzy matrix and discuss several properties. Further, we obtain sub-inverses and g-inverses of an intuitionistic fuzzy matrix using bi-implication operator